A Robust Approach to Possibility Single-Valued Neutrosophic  Dombi-Weighted Aggregation Operators for Multiple Attribute  Decision-Making

Yousef Al-Qudah; Ayman. A Hazaymeh; Faisal Al-Sharqi; Mamika Ujianita Romdhini; Sarah Jawad  Shoja

Authors

Yousef Al-Qudah Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, Jordan;
Ayman. A Hazaymeh Department of Mathematics, Faculty of Science, Jadara University, Irbid 21110, Jordan;
Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar,Ramadi, Anbar, Iraq;
Mamika Ujianita Romdhini Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram 83125, Indonesia;
Sarah Jawad Shoja College of Dentistry, Al-Ayen Iraqi University, An Nasiriyah, Iraq ;

Keywords:

Possibility single-valued neutrosophic number; Dombi operation; Possibility single-valued neu trosophic Dombi weighted arithmetic average (PSVNDWAA) operator; Possibility single-valued neutrosophic Dombi weighted geometric average (PSVNDWGA) operator; multiple attribute decision-making (MADM).

Abstract

Smarandache hands out the neutrosophic set (NS) theory that provides a general tri-mathematical
framework to avail oneself of handling uncertainties during the information analysis. In the NS-environment
there are three functions (T, I, F) that give a comprehensive description of each element or active case in the
universal set. In real-life applications such as decision-making, this description of the elements of the universal
set represents the decision-makers opinion, which must be objective and reliable.This decision-makers opinion,
which each of the three functions works to imagine, has no degree of acceptability, such as a degree of proba
bility of acceptance.This bar captures our attention and pay us to proposed a new notion of possibility single
value neutrosophic set (PSVNS) as a new view where every NS-membership function has a di erent degree
of probability of congruence (product).In this paper, based on PSVNN, the tools of Dombi t-norm (TN) and
Dombi t-conorm (TCN) are applied to initiate more exible and feasible operation rules for managing a param
eter in a PSVN-environment when We introduce the notion of PSVN-Dombi arithmetic average aggregation
(PSVDWAA) and PSVN-Dombi ordered weighted geometric aggregation (PSVNDWGA) operators.Due to the
PSVNDWAA and PSVNDWGA operators having the advantage of virtual pliability, we work to discuss their
di erent properties in addition to proofs, and also investigate multi-attribute decision-making (MADM) tech
niques according to proposed aggregation operators under PSVN-environment.Finally, an illustrative numerical
example about MACM that takes selecting an ideal bridge according to the standards required by the bridge
construction company to demonstrate the application and feasibility of the developed approach.